A half boundary method for two-dimensional nonlinear heat transfer problems in thermal barrier coatings

In the field of material surface modification, thermal barrier coatings (TBCs) are widely used to enhance the thermal insulation of high-temperature components such as gas turbine blades. Accurate heat transfer simulation is essential for evaluating TBC performance. This paper proposes the Half Boundary Method (HBM), a novel boundary-type numerical approach for heat transfer analysis in TBCs. HBM significantly reduces the computational memory usage by reducing the number of unknowns to only half of the boundaries. The theoretical foundation of HBM is derived and an iterative strategy is introduced to handle nonlinear problems involving temperature-dependent thermal conductivity. Numerical results show that HBM accurately models heat transfer in both single- and multi-layered structures. It is successfully applied to TBC-substrate systems with and without thermally grown oxides (TGOs), demonstrating its robustness and practical applicability. For the diffusion-reaction equation, HBM achieves excellent accuracy (maximum error: 0.1 %) even on coarse grids, with the number of unknowns increasing linearly with grid number. For the nonlinear TBC-substrate model, convergence is achieved within six iterations. These results indicate that HBM is highly accurate and effective, making it a promising tool for efficient thermal analysis and life prediction of critical components in complex TBC structures.